A plan of concurrent jurisdiction adopted under this chapter shall not include a delegation of any of the following:

    (a) A power of appointment to a public office delegated by constitution or statute to the circuit court or a circuit judge.

    (b) A power of appointment to a public office delegated by constitution or statute to the probate court or a probate judge.

    (c) A power of appointment to a public office delegated by law to the district court or a district judge, unless that power of appointment is delegated to a court or judge other than the circuit court or a circuit judge.